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Critical Behavior and Crossover Effects in the Properties of Binary and Ternary Mixtures and Verification of the Dynamic Scaling Conception

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Critical Behavior and Crossover Effects in the Properties of Binary and Ternary Mixtures and Verification of the Dynamic Scaling Conception Critical Behavior and Crossover Effects in the Properties of Binary and Ternary Mixtures and Verification of the Dynamic Scaling Conception Dissertation zur Erlangung des Doktorgrades der Mathematisch-Naturwissenschaftlichen Fakultaten¨ der Georg-August-Universitat¨ zu Gottingen¨ vorgelegt von Dipl. Phys. Ireneusz Iwanowski aus Sorau (Zary)˙ Gottingen¨ 2007 D7 Referent: Prof. Dr. Werner Lauterborn Korreferent: Prof. Dr. Christoph Schmidt Tag der mundlichen¨ Prufung:¨ 29.11.07 ...one of the strongest motives that lead men to art and science is escape from everyday life with its painful crudity and hopeless dreariness, from the fetters of one’s own ever-shifting desires. A finely tempered nature longs to escape from the personal life into the world of objective perception and thought. ALBERT EINSTEIN (1879-1955) Dla rodzicow´ Anny i Kazimierza Iwanowskich Contents 1 Introduction 1 2 Thermodynamics of Critical Phenomena 5 2.1 Phase transitions .............................. 5 2.2 Critical fluctuations ............................. 7 2.3 Critical phenomena ............................. 8 2.3.1 Critical exponents ......................... 8 2.3.2 Static scaling hypothesis ...................... 9 2.3.3 Dynamic scaling hypothesis and critical slowing down ...... 10 2.3.4 Renormalization of critical exponents ............... 12 2.3.5 Critical opalescence and equal volume criterions ......... 12 2.4 Phase diagrams ............................... 12 2.4.1 Phase diagrams for binary liquids at constant pressure ...... 12 2.4.2 Phase diagrams of ternary mixtures at constant pressure ..... 13 3 Experimental Methods 19 3.1 General aspects ............................... 19 3.2 Dynamic light scattering .......................... 20 3.2.1 Electromagnetic scattering theory ................. 20 3.2.2 Spectrum of scattered field - hydrodynamic considerations .... 22 3.2.3 Data evaluation of dynamic light scattering ............ 25 3.2.4 Self-beating spectroscopy ..................... 25 3.2.5 Technical equipment ........................ 27 3.3 Ultrasonic techniques ............................ 28 3.3.1 Classical absorption and background contribution ......... 29 3.3.1.1 Noncritical ultrasonic excess absorption ........ 30 3.3.1.2 Critical systems and total attenuation spectrum ..... 33 i Contents 3.3.2 Ultrasonic instruments ....................... 33 3.3.3 Resonator cells 80 kHz - 20 MHz ................. 34 3.3.4 Pulse-modulated traveling wave methods ............. 41 3.4 Complementary measurement techniques ................. 46 4 Critical Contribution, Dynamic Scaling and Crossover Theory 51 4.1 Bhattacharjee-Ferrell scaling hypothesis - binary systems ......... 51 4.2 Critical sound attenuation .......................... 51 4.3 The scaling function Fx(Ω) ......................... 56 4.4 The crossover theory in binary mixtures .................. 58 4.5 The crossover theory in ternary mixtures .................. 61 5 Experimental Verification of Dynamic Scaling Theories and Discus- sions 63 5.1 Strategies of verifying the scaling function ................. 63 5.2 Preparation of critical mixtures ....................... 66 5.3 Binary systems without and with one additional noncritical relaxation term 67 5.3.1 Phase diagram and critical temperature. .............. 68 5.3.2 Dynamic light scattering, shear viscosity ηs and characteristic re- laxation rate Γ0 ........................... 69 5.4 Fluctuation correlation length ........................ 74 5.5 Ultrasonic spectrometry ........................... 76 5.5.1 Scaling functions .......................... 79 5.5.2 Amplitude SBF and coupling constant g .............. 86 5.6 Systems with complex background contributions ............. 88 5.6.1 Isobutoxyethanol-water ....................... 89 5.6.2 2,6-dimethylpyridine-water .................... 92 5.6.3 Triethylamine-water ........................ 96 5.7 Ternary system nitroethane-3-methylpentane-cyclohexane ........ 104 5.7.1 Crossover studies of viscosity and light scattering ......... 107 5.7.2 Dynamic scaling function of a ternary mixture .......... 111 5.8 Summarized parameters and surface tension in critical mixtures ..... 118 6 Conclusions and Outlook 125 Literature I ii 1 Introduction Nature comprises a multitude of critical phenomena. Spontaneous symmetry breaking at the origin of the universe and gravitation collapse [1], [2] are spectacular examples. Crit- ical phenomena occur at phase transitions. Theories of phase transitions use methods of catastrophe theory and also of theory of percolation which currently attract considerable attention. In order to understand critical phenomena, investigations of liquid-liquid phase transi- tions in binary and ternary mixtures are very instructive. Especially the understanding of the phase behavior and the critical phenomena in ternary mixtures, biophysics and mem- brane physics have attracted attention during the last years [3], [4], [5]. The essential and most amazing feature of critical phenomena was the discovery of critical point universal- ity indicating that the microscopic structure of fluids becomes unimportant in the vicinity of the critical point. The understanding of such phenomena is also of great importance for chemistry and chemical engineering in procedures like liquid and solid extraction, drying, absorption, distillation and many other chemical reaction processes, as well as for biology in operations like fermentation, biological filtration and syntheses. Moreover, theories of critical phenomena are substantial for many innovative applications such as supercritical extraction, enhanced oil recovery and supercritical pollution oxidation. The importance of the understanding and application of critical phenomena is demonstrated by the recently (08.28.07) provided studies1 performed in the International Space Station (ISS). The fo- cus of those investigations were the critical phenomena, in particular the critical slowing down of the phase separation near the critical point of binary colloid-polymer mixtures in a micro gravity environment. The aim of such investigations was to develop fundamental physical concepts previously which had so far been masked by gravity effects. A first qualitative description of the critical behavior of some special systems was al- ready given at the beginning of last century. Examples are liquid/gas transition and the ferro/paramagnetism transition [6]. An essential step towards a deeper understanding of critical behavior was made by Landau’s general theory of phase transitions [7]. Later the theory has been further developed by Onsager, which found the exact solution [8] for 1National Aeronautics and Space Administration (NASA) Expeditions Assigned. Previous studies on crit- ical systems in micro gravity environment have been performed on in 1997 and 1998 on MIR, Source: http://www.nasa.gov. 1 1 Introduction the thermodynamic properties of a two-dimensional Ising model, that had been frequently discussed. It was a great surprise to find the theory of Landau to fail completely in predict- ing the behavior close to the critical point. Fisher, played a leading role by his analysis of experimental data, combining theoretical analysis and numerical calculations, [9], [10], [11]. Important theoretical contributions have been made by Widom [12], Patashinskii and Pokrovski [13], and most important by Kadanoff, [14]. Kadanoff put forward a very important new and original idea which seemed to have a strong influence on the later de- velopment of the field. However, his theory did not allow to calculate the critical behavior. The problem was solved in a comprehensive and profound way by Wilson [15]. Wilson was the first to realize that critical phenomena are different from most other phenomena in physics in that close to the critical point one has to deal with fluctuations over widely different scales of length. Nevertheless, investigations which have been performed on critical system have indicated the description of their behavior is not sufficient for a wide temperature range. The range between the background and mean-field behavior could not be described satisfactorily by classic theories of critical phenomena. Consequently, a new formalism has been developed by Albright [68], Burstyn, Sengers, Bhattacharjee and Ferrell, [16], [17], to describe the range between the consolute point and background behavior. This formalism is named crossover theory. The ideas of universality appear to be also applicable to phase transitions in complex fluids like polymers and polymer solutions, micro-emulsions and liquid crystals, fluids in porous media as well as phospholipid bilayer vesicle solutions. Besides dynamic light scattering an important measurement method to study the cooperative effects in complex fluids is the broad band ultrasonic spectroscopy. Being a non-destructive technique it al- lows for the measurement of chemical relaxations as well as critical fluctuations. During the past decades various theories have been developed to treat the critical slowing down of the critical ultrasonic attenuation in binary liquids within the framework of the dynamic scaling theory. The most prominent examples of the dynamic scaling theory have been presented by Bhattacharjee and Ferrell [18], [19], [20], [21], [22]. Folk and Moser [23], [24] developed a renormalization group theory of the mode-coupling model and Onuki [25], [26] derived a model from an intuitive description of the bulk viscosity near the critical point. The verification, with the aid of dynamic light scattering and shear
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